Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...

Sam Raskin in a still from the video “The Geometric Langlands Conjecture”. Credit: Institute for Advanced Study / Youtube Sam Raskin, a mathematician and professor at Yale University, has achieved a ...

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems. On September ...